psets/pset5sol.ipynb

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   "source": [
    "# 18.S190/6.S090 Problem Set 5 Solutions"
   ]
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    "## Problem 1\n",
    "\n",
    "Consider the following ordinary differential equation  \n",
    "\n",
    "$$\\frac{dx}{dt} = i x, \\quad x(0) = 1$$  \n",
    "\n",
    "where $i = \\sqrt{-1}$.  \n",
    "\n",
    "1. What is the analytical solution of the ODE at $t = \\pi$?  \n",
    "\n",
    "2. Write a code to numerically solve the ODE using forward Euler. What is the numerical solution at $t = \\pi$ with the following time step sizes?  \n",
    "   $\\Delta t = \\pi / 2^n, \\quad n = 0, 1, \\dots, 10$  \n",
    "\n",
    "3. Generate a **log-log** plot of the solution error (the absolute value of difference between the numerical and analytical solutions) at $t = \\pi$ versus $\\Delta t$. Describe what you observe in the plot.  \n"
   ]
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    "## Solution:\n",
    "\n",
    "**(1.1)**\n",
    "\n",
    "We consider the ODE  \n",
    "$$\n",
    "\\frac{dx}{dt} = i x, \\quad x(0)=1, \\quad \\text{where } i=\\sqrt{-1}.\n",
    "$$  \n",
    "Separating variables or recognizing it as a standard first-order linear ODE, we obtain the solution  \n",
    "$$\n",
    "x(t) = e^{i t}.\n",
    "$$  \n",
    "Evaluating at $t=\\pi$:  \n",
    "$$\n",
    "x(\\pi) = e^{i \\pi} = -1.\n",
    "$$  \n",
    "Thus, the analytical solution at $t=\\pi$ is $-1$.\n"
   ]
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    "**(1.2)** The following is a forward-Euler method, which prints out the approximate solution $x(\\pi)$ for timesteps $\\Delta t = \\pi /2^n$ as requested and prints out the value along with $n$:"
   ]
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   "execution_count": 1,
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    {
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     "output_type": "stream",
     "text": [
      "0 (1+3.141592653589793j)\n",
      "1 (-1.4674011002723395+3.141592653589793j)\n",
      "2 (-2.320597388556937+1.2037003610710544j)\n",
      "3 (-1.7553676637374411+0.2617424971050859j)\n",
      "4 (-1.3523575215265728+0.05339692774278987j)\n",
      "5 (-1.1658189293767178+0.01169964130484337j)\n",
      "6 (-1.0800532683412984+0.002721367899543206j)\n",
      "7 (-1.039293687670873+0.0006553749548332856j)\n",
      "8 (-1.0194620715000515+0.00016076084087411277j)\n",
      "9 (-1.0096846994337163+3.980745440099447e-05j)\n",
      "10 (-1.004830750680357+9.90418889498107e-06j)\n"
     ]
    }
   ],
   "source": [
    "# Part 2 (Numerical Solution Code)\n",
    "\n",
    "from pylab import *\n",
    "\n",
    "error = []\n",
    "\n",
    "for n in range(11):\n",
    "    dt = pi / 2**n   # time step size\n",
    "    x = 1            # initial condition\n",
    "    # Forward Euler update: x_{k+1} = x_k + i * x_k * dt\n",
    "    for i in range(2**n):\n",
    "        x = x + 1j * dt * x\n",
    "    print(n, x)                 # print n and the numerical approximation\n",
    "    error.append(abs(x + 1))    # error = |x - (-1)| = |x + 1|"
   ]
  },
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   "source": [
    "We can clearly see that the answer is getting closer to the correct value $x(\\pi) = -1$.   To be more quantitative, we now plot the convergence.\n",
    "\n",
    "**(1.3)** We now plot the error $|x(\\pi) + 1|$ vs. $\\Delta t$ for our approximate forward-Euler solutions, along with a first-order curve $\\sim \\Delta t$ for reference:"
   ]
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   "execution_count": 2,
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PddQ1mbnS7qOPPuL111/PNwEp7M9dQfXv358PP/yQuLg4Fi1axAMPPED58uWzHrfH627RogUTJkxg6dKlDBw4MGv/kiVLsh3n5+dHy5Yt2blzJ/Xq1cPLy+uq2rtUkyZNKFeuHO+99x49e/bMM7G6+eabufHGG9m1a1fWdS/OocRF8rVs2TJKlixJq1at2L17Ny+99BKhoaG5xqDz8sorr7By5UpatmzJyy+/TEBAAIsXL+aLL75gwoQJuQqAnThxggceeIDHHnuMM2fO8Morr+Dj48Pw4cPzbaN27dqMGTOGkSNHcvDgQdq2bUuFChU4fvw4W7Zswd/fP2spraPs2bOHPXv2AOYnw/Pnz2dVAQ4JCSEkJAQwx+/vvfdeXn75ZV5++WUAZs2axYYNG2jdujU1a9YkOTmZDRs2MG3aNJo0aULnzp2z2vn999/5z3/+Q2Rk5FXNcylfvjwvvfQSI0aMoG/fvkRERHDq1ClGjx6Nj48Pr7zySoHPde+99zJt2jR8fX1p2rQpYH7Cve6661i9ejWdOnXKtpT7/vvvZ/LkyfTq1YvHH3+cU6dO8dZbb2V11xfEkCFDmDNnDvfffz9jx46lSpUqLF68mL179xb8Tfif7du351mALiQkhLJly1K1alXuu+8+xo0bR4UKFQgODmbt2rUsW7bsiud25DU5efJkmjVrxp133smwYcO44YYbOH78OJ999hmzZs2iTJkyhf65K6jWrVsTFBTEoEGDOHbsWK7hOHu87rZt29K0aVOeffZZkpKSaNCgAT/88AMLFiwAsg83TZ06lWbNmtG8eXMGDhxI7dq1OXv2LL/++iuff/45X3/9daFeX+nSpZk0aRKPPvoo9913H4899hhVqlTh119/ZdeuXUyfPh0wf2bbtWtHmzZt6NevHzVq1ODvv//mv//9Lzt27OCjjz4qVLtylZw9O1hcT+ZKie3btxsdO3Y0SpcubZQpU8aIiIgwjh8/nu3Y4OBg4/7778/zPD/99JPRsWNHo1y5coaXl5cRGhqaa8lg5qz/hQsXGk899ZRRqVIlw9vb22jevHmu5ch5LT01DMNYsWKF0bJlS6Ns2bKGt7e3ERwcbHTv3t1Ys2ZN1jGRkZGGv79/rue2aNHCuPXWW3Ptv9zryiumvL4uXQWR+Tov3ff9998bHTp0MKpXr254eXkZfn5+RmhoqPHaa68ZycnJ2dop6HJow8h7VVGmDz74wKhXr57h5eVllCtXzujcuXO2paqGkf97lenTTz81AKNVq1bZ9j/22GMGYLzzzju5njNnzhzj5ptvNry9vY3rr7/eGDdunBEdHW0AxqFDh7KOu9z7vmfPHqNVq1aGj4+PERAQYDzyyCNZsVzrqiLAiI+Pzzo2MTHR6N69uxEQEGCUK1fOePjhh41t27YVaDm0YVzbNXk5e/bsMR588EEjMDDQ8PLyMmrVqmX069fPuHjxYtYxhfm5++ijj7Ltz2vlVKYRI0ZklS7Ib/XMtb7uv//+2+jfv79Rvnx5w8/Pz2jVqpWxadMmAzCmTp2aK9YBAwYYNWrUMEqVKmVUqlTJaNKkiTF27Nirfp1xcXFGixYtDH9/f8PPz88ICQnJtozcMMwl4g899JBRuXJlo1SpUkbVqlWNe+65x3jvvffyfE1ifxbDyDFzTYq9V199ldGjR/PXX3+5bIVRESkeYmJi6N27N99//z1NmjRxdjjiAjRUJCIiLiE2NpYjR45Qt25dSpQowaZNm5g4cSJ33323khbJosRFRERcQpkyZViyZEnWHdKrVatGv379GDt2rLNDExeioSIRERFxG6qcKyIiIm5DiYuIiIi4DSUuIiIi4jY8bnKuzWbj6NGjlClTpsDltEVERMS5DMPg7NmzVK9ePdf9rS7lcYnL0aNHc90ZVURERNzDH3/8cdkbXnpc4lKmTBnAfOEFueuqOE5aWhqrV6+mdevWlCpVytnhiIfQdSWOoOvK+ZKSkqhZs2bW3/H8eEziMmPGDGbMmEFGRgYAZcuWVeLiZGlpaVm3r9cvArEXXVfiCLquXMeVpnl4zOTcqKgo9uzZc823tBcRERHX5TGJi4iIiHg+jxkqKqyMjAzS0tKcHYZHS0tLo2TJkly8eDFrCE8KzsvL67Iz60VEiqNil7gYhsGxY8f4559/nB2KxzMMg6pVq/LHH39oafpVKFGiBNdddx1eXl7ODkVExGUUu8QlM2mpXLkyfn5++oPqQDabjXPnzlG6dGn1HBRSZj2ixMREatWqpetUROR/ilXikpGRkZW0BAYGOjscj2ez2UhNTcXHx0eJy1WoVKkSR48eJT09XascRET+p1j9Ncmc0+Ln5+fkSESuLHOISPODRET+VawSl0zqdhd3oOtURCS3YjVUJCIiIlcnIwM2bIDERKhWDZo3B6u16ONQ4iIiIiKXtWwZPP00/Pnnv/uCgmDqVOjatWhj8ZihohkzZhASEkLDhg2dHYqIiIjHWLYMunfPnrQAHDli7l+2rGjj8ZjERSX/RURE7Csjw+xpMYzcj2XuGzLEPK6oeEziUpQyMuCbbyA21vxXiz7s65tvvqF27dqFft6pU6eoXLkyv/32W4Gf0717dyZPnlzotuzhal+niEhRWb8+d0/LpQwD/vjDnPtSVJS4FNKyZVC7NrRsCb16mf/Wru34rrJ+/fphsVhyff3666/5Pta2bVvHBuVixo0bR8eOHQuVDLz88su8/vrrJCUl2TWW9evX07FjR6pXr47FYmHFihV2Pb+IiD0ZBhw/DuvWwfTpMHAgtGgBnToV7PmJiY6N71KanFsImeN8ObvMMsf5Pv7YsZOU2rZty9y5c7Ptq1SpUr6PeXt727X91NTUPMvP57f/as93NS5cuEB0dDRxcXGFel69evWoXbs2ixcvZuDAgVc8Pjw8nH79+tGvX7/LHpecnExoaCj9+/enW7duhYpJRMSRTpyA3bvNrz17/v3/qVNXf85q1ewX35UU68TFMOD8+YIdm5EBTz2V/zifxWKOA953X8GWh/n5mc8pDG9vb6pWrVrox/JjGAYTJ07kvffeIzExkZtuuomXXnqJ7t27A+Yf6dtuuw0vLy8WLFjArbfeyrfffpvv/pSUFJ5//nmWLFlCUlISd9xxB2PGjCE8PPyy5yuI2NhY+vfvz4EDB6hRowYAjz76KFu2bGHDhg2sXbuWkiVL0rhx42zPu+WWW/jll1/yPOfUqVN56qmn6NSpE7GxsQVKXAqqXbt2tGvXzm7nExEprBMnsicmmYnKyZN5H2+xwPXXQ0gI3Hqr+XXLLdClCxw9mvffP4vFXF3UvLlDX0o2xTpxOX8eSpe2z7kMwxwHLFeuYMefOwf+/vZp+2qNGjWKZcuW8e6773LjjTeyfv16Hn74YSpVqkSLFi0AmD9/PgMHDuT777/HuOSqzWv/Cy+8wCeffML8+fMJDg5m/PjxdOvWjf3791OxYsXLnu9KevbsyZtvvsm4ceOYPn06o0ePZtWqVWzatIly5cqxfv167rjjjlzPW758OSEhIaxdu5aQkBDS0tK4/vrriY2NpWPHjgA0atSIcePGkZKSYvdeKhGRvNizJspff+Xdg3K5BOW66/5NTjITlVtuMT9U5/TOO+aogsWSPXnJ/PA9ZUrR1nMp1omLu1m5ciWlL8m02rVrx0cffZTnYwAvvvgiL730Up7nSk5OZvLkyXz99ddZvRTXX3893333HbNmzcpKXG644QYmTJiQ6/k59ycnJ/Puu+8yb968rJ6G2bNnEx8fz5w5c3jhhRcue74rsVgsvP7663Tv3p3q1aszdepUNmzYkNX78ttvv1G9evVczzt27BglS5akadOmeHt7k5CQQHp6Os2bN89KUmrUqEFKSgrHjh0jODi40LGJiBTG1dZE+euvvHtQ/vor7+MvTVBy9qIU5s43XbuaUyHyinnKlKKv41KsExc/P7PnoyDWr4f27a98XFwc3H13wdourJYtW/Luu+9mbftf0mWT8zGAgICAfM+1Z88eLl68SKtWrbLtT01NpX79+lnbefVi5LX/wIEDpKWl0bRp06x9pUqVIiwsjP/+979XPF9BdOjQgZCQEEaPHs3q1au59dZbsx67cOECPj4+uZ7z008/cdNNN2UlKQkJCVSqVIkqVapkHePr6wvA+TzGDd944w3eeOONbO1s2rSJwYMHZ+378ssvaV6U/aQi4rYKMlfy7rtzJye7d+efoED2HpTMRKVOnav7W5OXrl2hc2dVznU6i6XgwzWtW5vZ5ZEjlx/na93acd9If39/brjhhkI/lhebzQbAF198kdVrkenS4RL/fN6gnPszh31y3l/HMIxs+/I7X0GsWrWKvXv3kpGRkS3xAKhYsSKnT5/O9Zwff/yRunXrZm0nJCRQr169bMf8/fffwL8TnS/15JNP8tBDD2Vt9+7dm27dutH1ko8YOd8/EZG8FKQmyoMPwv9+Pecpvx6Uoph6YLVCeLj596NECectSi7WiUthWK1mN54rjfNdi5CQELy9vTl8+HDWsNC1uOGGG/Dy8uK7776jV69egHk37oSEBIYMGXLN59+xYwcPPvggs2bNYsmSJbz00ktZw2QA9evXZ9GiRbme9+OPP9KlS5es7YSEBMLCwrId8/PPPxMUFJQ1D+dSAQEB2XqufH19qVy5cqGSRBERMHsrLlcTBf5NWmrXzrsHxdlzI+Pi4njuueeIj4932oc2JS6F4GrjfJfKnKNxqZIlS+b5xxigTJkyPPfcczzzzDPYbDaaNWtGUlISGzdupHTp0kRGRhaqfX9/fwYOHMjzzz9PQEAAtWrVYvz48Zw/f54BAwZc9esCc/7K/fffz7Bhw+jTp0/WrR22b99OgwYNAGjTpg3Dhw/n9OnTVKhQATA/FezevZuXX34561wHDx7kgQceyHb+DRs20Lp162uKMadz587x66+/Zm0fOnSIhISErPdGRIqfgtY6mTMH+vd3bCyFlZKSwvDhw3n77bcBeP3115k5c6ZTYlHiUkiuNM53qa+++opqORbS33zzzezduzff57z22mtUrlyZcePGcfDgQcqXL09YWBgjRoy4qhjefPNNbDYbffr04ezZs9xxxx188sknWYnE1fj7779p164dnTp1yoqrQYMGdOzYkZEjR/LVV18BULduXe644w4+/PBDnnjiCcCcd3P+/PlsQ0OhoaG8+uqr1K9fn7vvvpuLFy+yfPlyVq1addUx5mXbtm20bNkya3vo0KEAREZGMm/ePLu2JSKuLyUF1qwp2LHXXefYWApr37599OzZk507dwLw9NNPM378eOcFZHiYM2fOGIBx5syZXI9duHDB2LNnj3HhwgUnRFb8ZGRkGKdPnzYyMjIK9bx169YZwcHBhW7viy++MOrUqVOo9qZPn260atWq0G3Zw5Vep67XvKWmphorVqwwUlNTnR2KeBBHXldffWUYN9xgGOYkg/y/LBbDqFnTMNLT7R7CVbHZbMbcuXMNf39/AzAqVqxofP755w5r73J/vy/lMSX/dXdoad++PU888QRHjhwp8HNKlSrFtGnTHBiViBRXf/xhzots2xZ+/dXsoR8yxJwXmbMAqavNlUxKSqJ3797079+f5ORk7rnnHnbt2kWHDh2cHZrn3KtId4cWMLswa9asWeDjH3/8cW6++WYHRiQixU1qKowfb672+eQTMxF55hnYuxfeftucK5lzXmtQkONvG1NQmzdv5vbbbyc2Nhar1cq4ceNYvXp1nrWynEFzXMTl1K5d2y4rkVxdcXmdIsXJ119DVJSZpAA0awYzZsClVRhcda6kzWZj4sSJjBo1ivT0dGrXrk1sbCx33XWXcwPLQYmLuJzi8ge9uLxOkeLgyBF47jlYssTcrlwZJk6EPn3yvi9dZk0UV5GYmEjfvn1Z878ZxD169GDWrFmUK+h9bIqQxwwViYiIFLW0NJg0yRwWWrIESpSAwYPhl1+gb9/C30zXGeLi4qhXrx5r1qzBz8+POXPmEBsb65JJC6jHRURE5Kp8+605LLR7t7l9113msFCOGpcuK2dtlttvv50lS5a4/Lw/9biIiIgUwrFj5hBQeLiZtFSsCNHR8P337pO07Nu3j8aNG2clLU8//TSbNm1y+aQF1OMiIiJSIOnpMHMmvPQSJCWZw0BPPAGvvw6XuaetSzEMg/nz5zN48GCSk5OpWLEic+fOdYllzgWlxEVEROQKNm6EQYNg1y5z+447zCTGnUqHJSUl8eSTTxIbGwvAPffcw8KFC11mmXNBaahIREQkHydOwIAB0LSpmbRUqADvvQebNrlX0uLqtVkKQz0uIiIiOWRkwKxZMHIk/POPue+RR2DcOKhUyamhFYq71GYpDCUuIiIil9i82RwW2rHD3L79dnNYqHFjp4ZVaO5Um6UwNFTkZjZu3IjFYqFt27Z5Pj5kyBC6dOlStEGJiHiApKRSDBxopXFjM2kpVw6mTYNt29wvaclZmyU6Otqla7MUhhIXNzNnzhwiIiJYt24dhw8fzvX41q1badSokRMiExFxTzYbREdbiIq6j+joEhgGREaaReQGD3Z+Kf7CSElJ4ZlnnuH+++/n5MmThIaGsn37dgYMGIDFHarhFUCxHioyDIPz5887pW0/P79CX0TJycksXbqUtWvXcvr0aebNm8fLL78MQFpaGv7+/qSlpbFx40ZGjhxJo0aN2Lx5syPCFxHxCNu3m8NCW7aYfw5vu81g5kwLzZs7ObCr8Msvv9CzZ08SEhIAszbLm2++iY+Pj3MDs7NinbicP3+e0qVLO6Xtc+fO4e/vX6jnLF26lKpVq9KoUSN69+7NSy+9xEsvvYTFYsFqtfLdd99x5513kpCQQJUqVTzuYhURsZfTp2HUKHj3XTAMKFPG4MEHf2b69Fvw9S3l7PAKxTAM5s2bx+DBgzl//jyBgYHMmzfPrWqzFIaGitxIdHQ0vXv3BqBLly6cOHGCtWvXAlCiRAmOHj1KYGAgoaGhVK1alfLlyzsxWhER12Ozwdy5cNNN5oRbw4BeveCnn9Lp1OkgJd3s4/yZM2fo3bs3AwYM4Pz587Rs2ZIff/zRY5MWKOY9Ln5+fpw7d85pbRfGL7/8wsaNG5k7dy4ApUuXpnPnzsyZM4f77rsPgJ07dxIaGmr3WEVEPEFCgnlvoY0bze06dcx7C7Vsad4s8X8jLG5j8+bNREREcOjQIaxWK6+99hovvPACVnealHMVinXiYrFYCj1c4yzR0dE0bNiQm266KWtf79696datG6dPn6ZChQokJCQocRERyeHMGXj5ZZg+3exx8feHV16Bp58GLy9nR1d4NpuNCRMm8NJLL3lMbZbC8JihohkzZhASEkJDdyplWEDp6eksWLCAXr16Zdvfpk0bypQpw+LFiwH46aefqFevnjNCFBFxmowM+OYbiI01/83IMPcbBixaBDffDO+8YyYtDz0Ee/fC88+7Z9KSmJhI69atGT58OOnp6fTo0YOEhIRik7SAB/W4REVFERUVRVJSkkesU7/UypUrOX78OLfddhs///xztseaN29OdHQ0gwcPxmaz8eOPP3L06FH8/f097n0QEclp2TKz5+TPP//dFxQEzz4Ly5fD+vXmvptuMntcWrVyTpz2EBcXR2RkJCdPnsTPz49p06bRv39/j1nmXFAek7h4sujoaABaXeYnbseOHYwdO5YXX3yRt99+m6FDhzJp0qSiClFEpMgtWwbdu5s9K5f680945hnz/76+5t2chw4Fb++ij9EeUlJSGDZsGFOmTAEgNDSUJUuWcMsttzg3MCdR4uIGPv/88wIdFxYWxsMPP+zgaEREnC8jw+xpyZm0XMrXF37+Ga6/vujisrfiUpulMDxmjouIiBQfGzZkHx7Ky4ULkEeBcbdgGAZz584lLCyMhIQEAgMD+fzzz5kyZUqxTlpAPS4iIuKGEhPte5wrOXPmDAMHDiQ2NhaAli1bsmjRIqpXr+7kyFyDelxERMTtVKtm3+NcxebNm6lfvz6xsbFYrVbeeOMN4uPjlbRcQj0uIiLido4cufzjFou5ushd7jlU3GuzFEax7HExLjebS8RF6DoVyc0wYPRouHQdQs7VwJnbU6a4x52dVZulcIpV4lKqlHnjLGfdEVqkMFJTUwE8vny3SEFduAC9e8Orr5rbzz0HH30ENWpkPy4oCD7+GLp2LfIQCy0uLo569eqxdu1a/Pz8iI6OJjY2VnW4LqNYDRVZrVbKly/PiRMnAPN+QcWtcE9RstlspKamcvHiRUqUKFY58jWz2Wz89ddf+Pn5UdLd7vom4gDHj0OXLrBpE5QsCe+9B488Yj72wAPmKqPERHNOS/Pmrt/TotosV6/Y/UasWrUqQFbyIo5jGAYXLlzA19dXCeJVKFGiBLVq1dJ7J8XeTz9Bhw7m0uYKFeCTT8wbI2ayWiE83GnhFZpqs1ybYpe4WCwWqlWrRuXKlUlLS3N2OB4tLS2N9evXc/fdd2cN00nBeXl5qadKir24OOjRA86dgxtvhJUrzfL97sgwDObNm8fgwYM5f/48gYGBzJs3jw4dOjg7NLdS7BKXTFarVXMHHMxqtZKeno6Pj48SFxEpFMMwb4w4dKh5c8SWLc15KwEBzo7s6qg2i/3o45yIiLiUtDQYNAiGDDGTlkcega++ct+kRbVZ7KvY9riIiIjr+ecfeOghiI83lzVPnGj2urjjVC/VZnEMJS4iIuISDhwwJ+Hu3Qv+/hATA506OTuqq5OYmEifPn1Yu3YtAD169GDWrFla5mwHGioSERGnW78e7rzTTFqCguC779w3aVFtFsdS4iIiIk41fz7cdx+cOgUNG8KWLXD77c6OqvBSUlJ45plnuP/++zl58iShoaFs376dAQMGqKyBHSlxERERp7DZYPhw6NfPnJDbvTt884373RgRzNosd911V1ZBuaeffppNmzapoJwDaI6LiIgUueRk6NsXli0zt0eNMu9B5G6li1SbpegpcRERkSJ19Kg5f2X7dvDygujo7DdNdBeqzeIcbpbbioiIO9uxAxo1MpOWihXh66/dM2lRbRbnUeIiIiJFYsUK8waIR45ASAhs3gxNmzo7qsKx2WyMHz+eZs2acejQIWrXrs13333H8OHDVY29iChxERERhzIMmDABunaF8+ehTRvYuBGuv97ZkRVOYmIibdq0YdiwYaSnp9OjRw8SEhJUUK6IKXERERGHSU01S/a/+KKZwERFmTdKdLeSJpm1WdasWaPaLE6mybkiIuIQp06ZvSzr15urhaZOhcGDnR1V4aSkpDB8+HDefvttAEJDQ1myZImWOTuRS/a4rFy5kptvvpkbb7yRDz74wNnhiIhIIf3yi1kJd/16KFsWvvjC/ZKWffv20bhx46ykRbVZXIPL9bikp6czdOhQ1q1bR9myZQkLC6Nr164EuOttQUVEipm1a81icv/8A7Vrm0NDt97q7KgKzjAM5s+fz+DBg0lOTlZtFhfjcj0uW7Zs4dZbb6VGjRqUKVOG9u3bs2rVKmeHJSIiBTB7tjn59p9/oEkTc+WQOyUtSUlJ9O7dm/79+5OcnEzLli358ccflbS4ELsnLuvXr6djx45Ur14di8XCihUrch0zc+ZMrrvuOnx8fGjQoAEbNmzIeuzo0aPUqFEjazsoKIgjR47YO0wREbGjjAwYOhSeeML8/8MPmz0vlSs7O7KC27dvHw0bNlRtFhdn98QlOTmZ0NBQpk+fnufjS5cuZciQIYwcOZKdO3fSvHlz2rVrx+HDhwGziy4n3ZxKRMR1nT0LXbrA/6aC8NprsGAB+Pg4NawCs9lsTJw4keHDh6s2ixuw+xyXdu3a0a5du3wfnzx5Mo888giPPvooAFOmTGHVqlW8++67jBs3jho1amTrYfnzzz+588478z1fSkoKKSkpWdtJSUkApKWlkZaWdq0vR65B5vuv74PYk64r13L4MHTpUpKff7bg42MQHZ3Bgw8apKc7O7KCSUxMZMCAAaxduxaA7t278+6771KuXDldY0WsoO93kU7OTU1NZfv27QwbNizb/tatW7Nx40YAGjVqxM8//8yRI0coW7YscXFxvPzyy/mec9y4cYwePTrX/tWrV+Pn52ffFyBXJT4+3tkhiAfSdeV8+/ZV4I03GvHPP6UoX/4iI0Zsxt//H+LinB1ZwWzbto133nmHpKQkvL29eeyxx7j33nv5/vvvnR1asXT+/PkCHVekicvJkyfJyMigSpUq2fZXqVKFY8eOmQGVLMmkSZNo2bIlNpuNF154gcDAwHzPOXz4cIYOHZq1nZSURM2aNWndujVly5Z1zAuRAklLSyM+Pp5WrVpRqlQpZ4cjHkLXlWv48EMLL79s5eJFC3XrGixfbqVWrSbODqtAUlJSGDVqFFOnTgWgXr16zJs3j8OHD+u6cqLMEZMrccpy6JxzVgzDyLavU6dOdOrUqUDn8vb2xtvbO9f+UqVK6eJzEfpeiCPounIOwzDnsLzyirndsSMsXmyhTBn3+F7s27ePnj17snPnTsCszfLmm29itVo5fPiwrisnKuj7XqSJS8WKFbFarVm9K5lOnDiRqxdGRERcy8WLZvn+mBhz+9lnYfx4cIf5q1eqzaL5LO6jSOu4eHl50aBBg1xj0/Hx8TRp4h5djCIixdGJE3DPPWbSUrKkWa/lrbfcI2lRbRbPYvcel3PnzvHrr79mbR86dIiEhAQCAgKoVasWQ4cOpU+fPtxxxx00btyY2bNnc/jwYZ588slranfGjBnMmDGDjIyMa30JIiLFVkYGbNgAiYlQrRo0bw7//S906AC//w7ly8Mnn5hJjDvYvHkzERERHDp0CKvVymuvvcYLL7ygZc5uzO6Jy7Zt22jZsmXWdubE2cjISObNm0ePHj04deoUY8aMITExkdtuu424uDiCg4Ovqd2oqCiioqJISkrS3TpFRK7CsmXw9NPw55//7qtYEc6dM4eJbrjBvOfQTTc5L8aCyqzNMmrUKNLT06lduzaxsbHcddddzg5NrpHdE5fw8PA8i8hdatCgQQwaNMjeTYuIyFVatsy8v1DOX98nT5r/hoSYN0y8zCJPl5GYmEjfvn1Zs2YNAD169GDWrFn6UOshXO5eRSIiUrQyMsyelst95kxKMoeJXF1cXBz16tVjzZo1+Pn5ER0dTWxsrJIWD6LERUSkmNuwIfvwUF7+/NM8zlWlpKQwdOhQ7r//fk6ePEloaCjbt29nwIABum2Mh/GYxGXGjBmEhITQsGFDZ4ciIuJWEhPte1xR27dvH40bN+bt/90s6amnnmLTpk3ccsstTo5MHMFjEpeoqCj27NnD1q1bnR2KiIhbqVbNvscVFcMwmDdvHmFhYezcuZPAwEA+//xzpk6dio+73OFRCs0plXNFRMR1XGmYyGKBoCBzabSrSEpK4sknnyQ2NhaAli1bsmjRIqpXr+7kyMTRPKbHRURECscw4NVXoU+ff/flnA6SuT1liusUm9u8eTO33347sbGxWK1W3njjDeLj45W0FBNKXEREiqGLF6F3bxg92tx+4QX46COoUSP7cUFB8PHH0LVr0ceYk81mY/z48TRr1oxDhw5Ru3ZtvvvuO4YPH66CcsWIhopERIqZEyegSxf44QezfP9775n3IAJ44IHclXNdISdQbRbJ5DGJi0r+i4hc2e7dZvn+336DChXM8v2XFDvHaoXwcGdFl7e4uDgiIyM5efIkfn5+TJs2jf79+2uZczHlMUNFWlUkInJ5q1ZBkyZm0nLDDbBpU/akxdWoNovkxWMSFxERyd/MmXD//WYF3LvvNpMWV77nUM7aLE8//bRqswigxEVExKNllvOPijL/368fxMe77j2H8qvNMmXKFNVmEcCD5riIiEh2Z89Cz54QF2dujxsHL76Ye8mzq1BtFikIJS4iIh7o8GFzEu5PP4GvLyxcCN26OTuq/G3evJmIiAgOHTqE1Wrltdde44UXXtAyZ8lFiYuIiIfZsgU6dYLjx6FqVfjsM3DV27jZbDYmTpzIqFGjSE9Pp3bt2sTGxnLXXXc5OzRxUUpcREQ8yEcfQd++ZoG50FD4/HOoWdPZUeVNtVnkanjM5FzdHVpEijPDgNdfh4ceMpOWDh3MQnKumrTExcVRr1491qxZg5+fH9HR0cTGxippkSvymMRFdVxEpLhKSTFXC40aZW4/8wysWAFlyjgzqrypNotcKw0ViYi4sZMnzfsIbdhgVr2dPh2efNLZUeVt37599OzZk507dwJmbZY333xTy5ylUJS4iIi4qb17zSGhAwegXDlzfkurVs6OKjfDMJg/fz6DBw8mOTmZwMBA5s2bR4cOHZwdmrghJS4iIm5o7Vro3h3++Qeuuw5WroSQEGdHlZtqs4i9ecwcFxGR4uL996FtWzNpadoUNm92zaRl8+bN3H777cTGxmK1WnnjjTeIj49X0iLXRImLiIibyMiA556Dxx+H9HTo3RvWrIFKlZwdWXY2m43x48fTrFkzDh06RO3atfnuu+8YPny4CsrJNdNQkYiIGzh3zkxUPvvM3B4zxlxF5GoLcVSbRRzNYxKXGTNmMGPGDDIyMpwdioiIXf35J3TsCAkJ4O0N8+aZ9yByNXFxcURGRnLy5En8/PyYNm0a/fv31zJnsSuPGSpSHRcR8UTbt8Odd5pJS+XK8M03rpe0qDaLFCWPSVxERDzN8uVw991w9Cjceqs5CdfVbuGzb98+GjduzNtvvw2YtVk2bdrELbfc4uTIxFMpcRERcTGGARMmmHdzPn/eXEG0cSPUru3syP5lGAbz5s0jLCyMnTt3EhgYyOeff86UKVNUUE4cymPmuIiIeILUVBg4EObMMbcHD4a334aSLvTbWrVZxJlc6EdBRKR4+/tvs6jcunVQogRMmQL/93/Ojiq7zZs3ExERwaFDh7Barbz22mu88MILWuYsRUaJi4iIC9i/3yzfv2+feXPEJUugfXtnR/Uvm83GxIkTGTVqFOnp6dSuXZvY2FjucrVJN+LxlLiIiDjZt9+aN0r8+2+oVcss31+3rrOj+pdqs4gr0eRcEREnmjvXvDHi33+by543b3atpCUuLo569eqxZs0a/Pz8iI6OJjY2VkmLOI0SFxERJ7DZYNgwGDAA0tLgoYfMuS1Vqzo7MpNqs4irUuIiIlLEzp+HBx+E8ePN7VGjIDYWfH2dG1emffv20aRJE9VmEZfkMXNcVPJfRFxNRgZs2ACJiVCtGjRvDsePQ6dOZkVcLy/44APo08fZkZoMw2DBggVERUWRnJxMYGAg8+bNo0OHDs4OTSSLxyQuUVFRREVFkZSUpLFXEXG6Zcvg6afN+wxlqlLFvKvzqVMQGAgrVkCzZk4LMZukpCQGDhxITEwMoNos4ro8JnEREXEVy5aZ9VgMI/v+48fNf2vUMFcS/ec/RR9bXrZs2UJERAQHDx5UbRZxeUpcRETsKCPD7GnJmbTk5Arl+202G2+99RYjR47Mqs0SExND48aNnR2aSL40OVdExI42bMg+PJSXI0fM45wpMTGRNm3a8OKLL5Kens5DDz3Ezp07lbSIy1PiIiJiR4mJ9j3OEb788ktCQ0OzarN88MEHLFmyhPLlyzsvKJECUuIiImJH1arZ9zh7yqzN0r59e/766y9CQ0PZtm0bjzzyiGqziNvQHBcRETvav//yj1ssEBRkLo0uSvv27SMiIoIdO3YA8NRTTzF+/Hh8fHyKNhCRa6QeFxERO0hNhUGD4PHH/92XsxMjc3vKFCiqBTuGYTB//nzCwsLYsWMHgYGBfPbZZ0ydOlVJi7glJS4iItfo2DG49154910zORkzBj76yFz2fKmgIPj4Y/OGikUhKSmJhx9+mH79+pGcnEzLli3ZtWsXHTt2LJoARBxAQ0UiItdg82bo1s1cKVS2LCxeDJmFZh94IHfl3KLqaclZm2XMmDG8+OKLqs0ibk+Ji4jIVZozBwYONIeJ6tQxK+HedNO/j1utEB5etDHlrM0SHBxMbGysljmLx1DiIiJSSKmpMGSIOTQE0KULzJ9v9rg4U2JiIn379mXNmjUAPPTQQ8yaNUvLnMWjeMwclxkzZhASEkLDhg2dHYqIeLC85rN88onzkxbVZpHiwmMSl6ioKPbs2cPWrVudHYqIeKjNm+GOO+C778xE5bPP4KWXoIQTf5OqNosUNx6TuIiIONKcOXD33eYk3Dp1YOvWfyfhOsu+ffto0qQJb7/9NmDWZtm0aRN16tRxbmAiDqTERUTkMjLrszzyiPn/Ll1g06bsk3CLmmqzSHGmybkiIvk4dgwefNAcGrJYYPRoGDnSuUNDSUlJDBw4kJiYGABatmzJwoULqZGzaIyIh1LiIiKShy1bzEJxedVncV5Mqs0ioqEiEZEc5swxi8W5ynwWm83GhAkTaNq0KQcPHiQ4OJgNGzYwYsQIJS1S7KjHRUTkf1JT4ZlnYOZMc9sV6rPkrM3y4IMPMnv2bC1zlmJLPS4iIsDx42Z9lsykZfRo59dnubQ2i6+vLx988AFLly5V0iLFmnpcRKTYc7X5LCkpKQwfPjxrmXO9evVYsmSJljmLoB4XESnmLp3PcsstZhLjzKQlZ22W//u//2Pz5s1KWkT+R4mLiBRLqakQFfVvfZbOnc3KuDff7Jx48qvN8s4776g2i8glNFQkIsXO8ePQvbtZnwXM+SyjRjmvPkvO2izh4eEsWrRItVlE8qDERUSKFVebz5KzNsvo0aMZNmyYljmL5ENDRSJSbLjSfJa8arOsX7+ekSNHKmkRuQz1uIiIx8tZn6VzZ1iwwHlLnVWbReTqqcdFRDxaXvVZli1zXtKi2iwi10Y9LiLisVxpPotqs4jYh3pcRMQjzZ0Ld9/tGvNZctZmGTx4sGqziFwlJS4i4lHS0mDwYBgwAFJSoFMn59Vnya82y7Rp01SbReQqeUziMmPGDEJCQmjYsKGzQxERJ8mczzJjhrk9ejQsX+6c+SxJSUk8/PDD9OvXj+TkZMLDw9m1axcdO3Ys+mBEPIjHJC5RUVHs2bOHrVu3OjsUEXGCLVugQQPYsMFMVD77DF5+2TlF5bZs2UL9+vWJiYnBarUyduxY1qxZo4JyInagybki4vbmzoWBA82hoVtugRUrnDM0ZLPZeOuttxg5ciTp6ekEBwcTExNDkyZNij4YEQ+lxEVE3EJGhtmb8scfFn7/PZA2bcz9zzzz79BQp06wcKFzhoZUm0WkaChxERGXt2wZPP00/PknmL+2mjFzpkH58vDf/5rHOPN+Q19++SWRkZH89ddf+Pr6Mm3aNAYMGIDFYin6YEQ8nBIXEXFpy5aZN0Q0jOz7ExPNL19fWLoUnDHnVbVZRIqeEhcRcVkZGWZPS86kxWT2ZpQrB+3bF2lYgFmbJSIigh07dgDwf//3f0yYMEHLnEUczGNWFYmI59mwIXN4KH/HjpnHFZX8arO88847SlpEioB6XETEZSUm2ve4a5WUlMTAgQOJiYkBIDw8nEWLFmmZs0gRUo+LiLisatXse9y1UG0WEdegHhcRcUkZGbB27eWPsVggKAiaN3dcHKrNIuJalLiIiMv56y/o1Qv+VxIFMJOUSyfpWiwGYGHKFLBaHROHarOIuB4NFYmIS9m4EerXN5MWPz+zoNwnn0DOEZkaNeDjj6FrV8fE8eWXXxIaGsqaNWvw9fXlgw8+YOnSpUpaRJxMPS4i4hIMA6ZMgRdegPR0s2T/J5/Arbeaj3funFk5N53ff9/Ec8/diY9PKbvHodosIq5NiYuIOF1SEgwYYCYqAD16wPvvQ5ky/x5jtUJ4OKSlGcTFnXLI8JBqs4i4PiUuIuJUP/5oVsbdvx9KlYLJkyEqypzTUlQMw2DBggVERUWRnJxMYGAgc+fOpaMzyvGKyGUpcRERp5k3z7yr88WLULMmfPQR3Hln0cag2iwi7kWTc0WkyF24AI8+Cv37m0lL27awc2fRJy2qzSLiftTjIiJF6tdfzaGhXbvM4aAxY2DEiKK9q7Nqs4i4LyUuIlJkli+Hfv3MybiVKkFMDNx3X9HGoNosIu5NQ0Ui4nBpafD882bNlaQkaNrUHBoq6qRFtVlE3J8SFxFxqKNH4Z574K23zO2hQ2HdutwF5RwpJSWFoUOH0r59e/766y/q1avH9u3beeSRR7AU5fIlEblmGioSEYf5+muIiIATJ6BsWZg713GVbvOj2iwinkU9LiJidzYbvPEGtGplJi316sG2bUWbtBiGwfz58wkLC2PHjh0EBgby2Wef8c477yhpEXFj6nEREbs6dQr69oW4OHN7wACYPh18fYsuBtVmEfFc6nEREbvZsgXCwsykxccHoqPNr6JMWlSbRcSzqcdFRK6ZYcC778KQIeYKohtuMO/cHBpadDGoNotI8eCSPS4PPPAAFSpUoHv37s4ORUSu4Nw56N3bvL9QWpo5j2XbtqJNWhITE2nTpg0vvvgi6enpPPjggyQkJChpEfFALpm4PPXUUyxYsMDZYYjIFezZA40aQWyseffmSZPMnpZy5YouBtVmESleXDJxadmyJWUuvZ+9iLicmBho2BD++1+oXh2++cas0VJUZVFUm0WkeCp04rJ+/Xo6duxI9erVsVgsrFixItcxM2fO5LrrrsPHx4cGDRqwYcMGe8QqIi4gJQUGDTKHh86fh3vvNavgNmtWdDEcOXKEu+++m7fffhswa7Ns3ryZOnXqFF0QIuIUhZ6cm5ycTGhoKP3796dbt265Hl+6dClDhgxh5syZNG3alFmzZtGuXTv27NlDrVq1AGjQoAEpKSm5nrt69WqqV69eqHhSUlKynSspKQmAtLQ00tLSCnUusa/M91/fB8/x228QEWFl+3bzM8+IERm89JINq9Wc3+JohmEwb948nn32WS5evEhgYCDvv/8+HTp0AHStydXT7yvnK+h7bzEMw7jaRiwWC8uXL6dLly5Z++68807CwsJ49913s/bVqVOHLl26MG7cuAKf+5tvvmH69Ol8/PHHlz3u1VdfZfTo0bn2x8TE4OfnV+D2ROTytm2rwpQpYZw750WZMqkMGbKdBg1OFFn758+f57333mP9+vUA3HbbbTzzzDMEBgYWWQwi4jjnz5+nV69enDlzhrJly+Z7nF2XQ6emprJ9+3aGDRuWbX/r1q3ZuHGjPZvKMnz4cIYOHZq1nZSURM2aNWnduvVlX7g4XlpaGvHx8bRq1YpSpUo5Oxy5SunpMHp0CcaPtwLQsKGN2FgLtWrdUWQxbN26lT59+nDw4EGsVis9e/bk3XffVQVcsRv9vnK+zBGTK7Fr4nLy5EkyMjKoUqVKtv1VqlTh2LFjBT5PmzZt2LFjB8nJyQQFBbF8+XIaNmyY57He3t54e3vn2l+qVCldfC5C3wv3dfy4ea+hdevM7cGD4a23SuDtXTTz+vOqzbJgwQJOnz6Nj4+PriuxO/2+cp6Cvu8OKUCXc0a/YRiFmuW/atUqe4ckIoW0YQP06AGJieDvDx98AD17Fl37iYmJREZGEh8fD8CDDz7I7Nmz8ff3Jy7zfgIiUuzY9WNTxYoVsVqtuXpXTpw4kasXRkRck2HAW29By5Zm0hISAlu3Fm3SklmbJT4+XrVZRCQbuyYuXl5eNGjQIOsTUqb4+HiHV7CcMWMGISEh+Q4piciV/fOPWfn2+echI8Nc8rxlCxTVKmPVZhGRKyn0UNG5c+f49ddfs7YPHTpEQkICAQEB1KpVi6FDh9KnTx/uuOMOGjduzOzZszl8+DBPPvmkXQPPKSoqiqioKJKSkihXlGU7RdxQRoY5FJSYCNWqQfPm8OOP0L07HDwIXl7wzjvw+ONFV1Bu3759REREsGPHDsCszTJhwgRNwBWRbAqduGzbto2WLVtmbWeu6ImMjGTevHn06NGDU6dOMWbMGBITE7ntttuIi4sjODjYflGLyFVbtgyefhr+/PPffRUqwNmz5gqi2rXNsv0NGhRNPIZhsGDBAqKiokhOTiYwMJC5c+fSsWPHoglARNxKoROX8PBwrlT6ZdCgQQwaNOiqgxIRx1i2zOxVyfkjfPq0+W+DBrB6NQQEFE08SUlJDBw4kJiYGMD8/bJo0SJq1KhRNAGIiNtxyXsViYj9ZWSYPS2X+9xx4kTR3SBxy5Yt1K9fn5iYGKxWK2PHjmXNmjVKWkTkspS4iBQTGzZkHx7Kyx9/mMc5ks1mY8KECTRt2pSDBw8SHBzM+vXrGTlyJFar1bGNi4jbc0gdF2eYMWMGM2bMICMjw9mhiLikxET7Hnd1MSTSt29f1qxZA/xbm0XLnEWkoDymxyUqKoo9e/awdetWZ4ci4pIKeu+4atUc035mbZY1a9aoNouIXDWPSVxEJH8xMXCl+fIWC9SsaS6NtifVZhERe1LiIuLBLlyAxx4zC8klJ8Ott5oJSs58IXN7yhSw5zSTffv20aRJE95++23ArM2yefNm6hRVRTsR8ThKXEQ81N690KiReY8hiwVefhl27TJrtORcuBMUZO7v2tU+bRuGwfz58wkLC2PHjh0EBgby2Wef8c4776ignIhcE4+ZnCsi/1q4EAYONHtZqlSBxYvh3nvNx7p2hc6dc1fOtVdPi2qziIgjeUziolVFInD+PAweDHPnmtv33GMmLVWrZj/OaoXwcPu3v2XLFiIiIjh48CBWq5XRo0czbNgwLXMWEbvxmKEirSqS4m7PHmjY0ExaSpSA0aPNKrg5kxZHUG0WESkqHtPjIlKczZsHUVFmj0vVquYqoktuKeZQqs0iIkXJY3pcRIqj5GSIjIT+/c2kpVUrSEgouqRFtVlEpKgpcRFxUz//DHfcAQsWmENDY8fCV1+Zk3EdTbVZRMRZNFQk4mYMA+bMgf/7P7NOS/XqEBsLd99dNO3v27ePiIgIduzYAZi1WSZMmKBlziJSJJS4iLiRc+fgySfNlUIAbdqYS58rVXJ824ZhsGDBAqKiokhOTiYwMJC5c+fSsWNHxzcuIvI/SlxE3MSPP8JDD8Evv5jLmceOhRdeMIeJHC0pKYlBgwax+H8Zk2qziIizeMwclxkzZhASEkLDhg2dHYqIXRkGzJ4Nd95pJi01asA338CwYUWTtGzZsoX69euzePFirFYrY8eOZc2aNUpaRMQpPCZxUR0X8URJSdCrFzzxBFy8CO3bm6uGmjVzfNuqzSIirkhDRSIuKiHBHBrav98cGho3Dp59tmh6WY4dO0bfvn2Jj48HVJtFRFyHx/S4iHgKw4B334W77jKTlpo1Yf16eP75oklavvzyS+rVq0d8fDy+vr68//77qs0iIi5DiYuICzlzBnr2hEGDICUFOnaEnTuhSRPHt52SksKzzz6bqzbLo48+qtosIuIyNFQk4iJ27DCHhg4cgJIlYfx4eOYZKIqcIWdtlsGDBzNx4kTVZhERl6PERcTJDANmzDDnr6SmQnAwLFliDhU5vm2DhQsXMmjQIJKTkwkICGDu3Ll06tTJ8Y2LiFwFJS4iTnTmDDzyCHzyibndubN5d+cKFRzftmqziIg78pg5LqrjIu5m2zaoX99MWkqVgilTYPnyoklaVJtFRNyVxyQuquMi7sIwYOpUc8LtoUNQuzZ8/z08/bTj57OoNouIuDsNFYkUodOnYcAAWLHC3O7aFaKjoShWGqs2i4h4Ao/pcRFxdVu2QFiYmbR4ecG0afDxx0WTtKg2i4h4CiUuIg5mGDB5MjRtCr/9BtdfDxs3wuDBjh8aUm0WEfE0GioScaC//4b+/eGzz8ztBx+E99+HcuUc37Zqs4iIJ1LiIuIgP/xgVsE9fNgcGnr7bRg40PG9LKrNIiKeTImLyDXKyIANGyAxEapVM4eEpkyBESMgPR1uuAE+/NBc+uxoedVmWbhwIUFBQY5vXESkCChxEbkGy5aZy5j//PPffT4+cPGi+f8ePWD2bChb1vGxbNmyhYiICA4ePIjVamX06NEMGzZMy5xFxKMocRG5SsuWQffu5uTbS2UmLU88Yd7luShqs7z11luMHDmS9PR0goODiYmJoUlR3JlRRKSIKXERuQoZGWZPS86kJZPFAnFxYLOBIzs8VJtFRIobj1kOrZL/UpQ2bMg+PJSTYcAff5jHOYpqs4hIceQxiYtK/ktRSky073GFodosIlKcaahIpJDS081hoIKoVs2+bas2i4gUd0pcRArhjz+gVy/47rvLH2exQFAQNG9un3ZVm0VExOQxQ0UijvbZZ3D77WbSUqYMDB1qJig5R2cyt6dMsc/E3KSkJPr06UNkZCTJycmEh4fz448/KmkRkWJJiYvIFaSkwJAh0LmzWcL/jjtg506YNMm8SWKNGtmPDwoy93fteu1tb9myhfr167N48WKsVitjx45lzZo11MjZqIhIMaGhIpHL2L/fLNv/vyklPPMMvPmmWcIfzOSkc+fslXObN7/2nhbVZhERyZsSF5F8xMSYReTOnYPAQJg3Dzp0yH2c1Qrh4fZrV7VZRETyp6EikRySk+GRR6B3bzNpuftuSEjIO2mxN9VmERG5PCUuIpf46Sdo2BDmzDEn2b7yCnz9tTlvxZFUm0VEpGA0VCSCWel29mxzEu7Fi+ZclZgY+w4B5Ue1WURECk6JixR7//wDjz8OH31kbrdrB/PnQ6VKjm1XtVlERApPiYsUa1u2QI8e8NtvULKkuWLomWeghIMHUZOSkhg0aBCLFy8GIDw8nEWLFmmZs4jIFXjMHBfdZFEKw2aDt96Cpk3NpOW66+D77+HZZx2ftKg2i4jI1fOYxEU3WZSC+usvc4XQ88+b9x168EGzoFyjRo5t12azMWHCBJo2bcrBgwcJDg5m/fr1jBw5Eqs9SuyKiBQDGiqSYmXdOnOZc2Ii+PjA1Knw2GO5y/bbm2qziIjYh8f0uIhcTnq6ubT53nvNpKVOHXN+y+OPOz5pUW0WERH7UY+LeLw//zR7WdavN7cfecTsafH3d2y7KSkpjBgxgsmTJwNQr149lixZQp06dRzbsIiIB1PiIh5t5Uro1w9OnYLSpc1aLRERjm9XtVlERBxDQ0XikVJTYehQ6NjRTFrCwswJuI5OWgzDYMGCBYSFhbFjxw4CAgL49NNPmTZtmpIWERE7UI+LeJwDB8w7Om/bZm4//TSMHw/e3o5tV7VZREQcTz0u4lGWLIH69c2kJSAAPv0UpkxxfNKi2iwiIkVDPS7iEc6fN3tWPvjA3G7WzLzXUM2ajm3XZrPx1ltvMXLkSNLT0wkODiYmJoYmTZo4tmERkWJKiYu4vd27zbL9u3ebS5tHjjSXPpd08NWt2iwiIkVPiYu4LcMwe1iefhouXICqVWHxYrjnHse3/eWXXxIZGclff/2Fr68vU6dO5dFHH8Xi6KIwIiLFnBIXcUtnzsATT8DSpeZ2mzawYAFUruzYdnPWZqlbty5LliwhJCTEsQ2LiAigybnihrZuNZc3L11qDgdNmABxcY5PWvbt20eTJk2ykpbBgwezZcsWJS0iIkVIPS7iNgwD3n4bhg2DtDSoXRtiY+GuuxzdrsHChQsZNGgQycnJBAQEMGfOHDp37uzYhkVEJBclLuIWTp40K+B+8YW53a2bOb/F0fNgc9ZmadGiBYsWLSIoKMixDYuISJ6UuIhLyciADRvMGyFWqwbNm8P330OvXnDkiFmP5e234cknHX9zxK1bt9KzZ08OHjyI1Wrl1VdfZfjw4VitVsc2LCIi+VLiIi5j2TJzhdCff/67r2xZOHvWHCa6+WZzXktoqGPjsNlsTJo0iREjRpCenk6tWrWIiYmhadOmjm1YRESuSImLuIRly6B7dzNBuVRSkvlvy5bw+eeOv6Nzztos3bt3Z/bs2VSoUMGxDYuISIFoVZE4XUaG2dOSM2m51K+/gqPvUfjVV18RGhpKfHw8vr6+zJ49mw8//FBJi4iIC/GYxGXGjBmEhITQsGFDZ4cihbRhQ/bhobz88Yd5nCOkpqby3HPP0a5dO06cOEHdunXZtm0bjz32mArKiYi4GI9JXKKiotizZw9bt251dihSSImJ9j2uMPbv30+TJk2YNGkSoNosIiKuTnNcxOl27y7YcdWq2bfdBQsWqDaLiIibUeIiTpOcDP/3fzB37uWPs1ggKMhcGm0PSUlJREVFsWjRIkC1WURE3InHDBWJe0lIgAYNzKSlRAl46CEzQck5pSRze8oUsEf5lK1btxIWFsaiRYuwWq289tprrF27VkmLiIibUOIiRcowYPp0s0z/L79AjRrw9ddmfZaPPza3LxUUZO7v2vXa2rXZbEycOJEmTZpw4MABatWqxbfffsuoUaNUUE5ExI1oqEiKzN9/w4AB8Omn5nbHjjBnDlSsaG537QqdO+eunHuteYVqs4iIeA4lLlIkNmwwy/b/+Sd4ecHEieb8lpxDQ1YrhIfbr92vvvqKyMhITpw4ga+vL1OnTuXRRx/VMmcRETeloSJxqIwMGDu2BOHhZtJy442waRM89ZRj7zWk2iwiIp5JPS7iMEeOwMsvN2X3bnOsJzLSnN9SurRj292/fz8RERFs374dMGuzTJw4ER9Hl94VERGHU4+LOMTKlXDHHSXZvbsipUsbLFwI8+Y5PmlZsGAB9evXZ/v27QQEBLBixQqmTZumpEVExEOox0XsKiUFXnwRpk4FsHD99f/w+ef+hISUcmi7qs0iIlI8KHERu9m3D3r2hJ07ze2nnsqgefMN3HhjW4e2u3XrViIiIjhw4ABWq5VXX32V4cOHa5mziIgH0lCR2MXChRAWZiYtgYHmUNFbb9koVcrmsDZVm0VEpPhRj4tck7NnISrKTFzAXMq8aJFZSC4tzXHtqjaLiEjxpB4XuWo7dphl+xcuNMv2v/YarFmTu/qtvX311VeEhoYSHx+Pr68vs2fP5sMPP1TSIiJSDKjHRQrNMOCdd+D5581elZo1ISYGmjVzbLupqamMGDGCSZMmAVC3bl2WLFlCSEiIYxsWERGXocRFCuXkSejf35zDAtClC0RHQ0CAY9tVbRYREQENFUkhfPMNhIaaSYu3N8yYAcuWOT5pUW0WERHJpB4XuaL0dBgzBsaONYeJbrkFliwxkxhHUm0WERHJST0ucll//AEtW5oTbw3DvLvztm2OT1q2bt1KWFgYixYtokSJEowZM4a1a9cqaRERKebU4yL5+vRTcz7L6dNQpgzMmgUREY5t02azMWnSJEaMGEF6ejq1atUiJiaGpk2bOrZhERFxC0pcJJeLF80VQ9Onm9sNG0JsLPznP45t99ixY0RGRrJ69WoAunXrxvvvv69lziIikkVDRZLN3r1w113/Ji3PPQfffef4pCWzNsvq1auzarN89NFHSlpERCQb9bgIYM5fmTcPBg+G8+ehUiVYsADaOvY2Q6rNIiIihaLERUhKgoEDzSJyAPfea1bDrVbNse3mrM0SFRXFxIkT8fX1dWzDIiLitjRUVMxt22beHDEmBqxWeOMNWL3a8UlLXrVZpk+frqRFREQuy+USlz/++IPw8HBCQkKoV68eH330kbND8kg2G0yaBE2awIEDEBwM69fD8OHmfYccJSkpiT59+hAZGUlycjItWrRg165ddO7c2XGNioiIx3C5oaKSJUsyZcoUbr/9dk6cOEFYWBjt27fH39/f2aF5jBMnIDISvvrK3O7WDT74AMqXd2y7W7duJSIiggMHDlCiRAleffVVRowYgdVqdWzDIiLiMVwucalWrRrV/jdOUblyZQICAvj777+VuFyFjAzYsAESE82hn+bNzbL9Dz8Mx46Bjw9MmQKPPw4Wi+PisNlsTJw4UbVZRETkmhV6UGD9+vV07NiR6tWrY7FYWLFiRa5jZs6cyXXXXYePjw8NGjRgw4YNVxXctm3bsNls1KxZ86qeX5wtWwa1a5tVb3v1Mv+tUAHuu89MWkJCYOtWeOIJxyYtp0+fpkOHDrzwwgukp6fTvXt3EhISlLSIiMhVKXSPS3JyMqGhofTv359u3brlenzp0qUMGTKEmTNn0rRpU2bNmkW7du3Ys2cPtWrVAqBBgwakpKTkeu7q1aupXr06AKdOnaJv37588MEHl40nJSUl27mSkpIASEtLIy0trbAvzyMsX26hZ08rhgHwb1Zy9qz57733ZvDJJzb8/MCRb9EXX3zBkCFDOHPmDL6+vkyePJkBAwZgsViK7fdGrl3mtaNrSOxJ15XzFfS9txiG+eftalgsFpYvX06XLl2y9t15552EhYXx7rvvZu2rU6cOXbp0Ydy4cQU6b0pKCq1ateKxxx6jT58+lz321VdfZfTo0bn2x8TE4OfnV7AX4kEyMuDxx1tz6pQPlyYt/zKoWPECs2bF46ipJWlpaSxatIhPP/0UgODgYJ577jn1nImISL7Onz9Pr169OHPmDGXLls33OLvOcUlNTWX79u0MGzYs2/7WrVuzcePGAp3DMAz69evHPffcc8WkBWD48OEMHTo0azspKYmaNWvSunXry75wT/XttxZOnbrct9XCyZN+lC17Py1aXHXOmq/9+/fTp08fduzYAUD79u1ZuHAhZcqUsXtbUjylpaURHx9Pq1atKFWqlLPDEQ+h68r5MkdMrsSuicvJkyfJyMigSpUq2fZXqVKFY8eOFegc33//PUuXLqVevXpZ82cWLlxI3bp18zze29sbb2/vXPtLlSpVLC++v/4q6HElsffbs2DBAgYNGkRycjIBAQHMnj2bkiVLUqZMmWL5vRDHKq4/4+JYuq6cp6Dvu0NWFVlyzPY0DCPXvvw0a9YMm83miLA8nmGYE24Lwp4F5pKSkoiKimLRokUAtGjRgkWLFlGlShXi4uLs15CIiBR7di01VrFiRaxWa67elRMnTuTqhRH7On0aHnwQ3n778sdZLFCzprk02h62bt1KWFgYixYtwmq18tprr7F27VqCgoLs04CIiMgl7Jq4eHl50aBBA+Lj47Ptj4+Pp0mTJvZsKpcZM2YQEhJCw4YNHdqOK/r+e7j9dvjkEyhVyiwuZ7HkXuacuT1lCtc8MTezNkuTJk04cOAAtWrV4ttvv2XUqFEqKCciIg5T6MTl3LlzJCQkkJCQAMChQ4dISEjg8OHDAAwdOpQPPviAOXPm8N///pdnnnmGw4cP8+STT9o18JyioqLYs2cPWws6VuIBMjJg7Fho0QIOH4b//Ac2bjTv8vzxx1CjRvbjg4LM/V27Xlu7x44do23btqrNIiIiRa7Qc1y2bdtGy5Yts7YzV/RERkYyb948evTowalTpxgzZgyJiYncdtttxMXFERwcbL+ohSNHoE8fWLfO3O7dG2bOhMyFVF27QufOuSvnXmtnyFdffUVkZCQnTpzA19eXqVOn8uijjxZ4DpOIiMi1KHTiEh4ezpVKvwwaNIhBgwZddVByeStXQr9+cOoU+PubCUvfvrmPs1ohPNw+baampjJixAgmTZoEQN26dVmyZAkhISH2aUBERKQAXO5eRZK/lBR44QV45x1zu359WLIEbrrJse3u37+fiIgItm/fDsDgwYOZOHEiPj4+jm1YREQkByUubuKXX6BnT/jf1CKGDIE334Q8StjYVc7aLHPmzKFz586ObVRERCQfdl1V5EyeuqrIMMzJtg0amElLxYrmUNHbbzs2aUlKSqJPnz5ERkaSnJxMixYt2LVrl5IWERFxKo9JXDxxVVFSEjz8MPTvD8nJcM89sGsX3H+/Y9u9tDZLiRIlGDNmjGqziIiIS9BQkYvautUcGjp40JxkO2YMvPjita8KuhybzcakSZMYMWIE6enp1KpVi5iYGC1zFhERl6HExcXYbDBpEowYAenpEBwMMTHg4Pp9HDt2jL59+2YVD+zWrRvvv/8+FSpUcGzDIiIihaDExYUcP25WvV21ytzu3h3efx/Kl3dsu6rNIiIi7sJj5ri4u9WroV49M2nx9YXZs+HDDx2btKSmpvLcc8/Rrl07Tpw4Qd26ddm2bRuPPfaYkhYREXFJHpO4uOuqotRUszZLmzZw4gTcdhts2waPPZb7XkP2tH//fpo0aZJVUC4qKorNmzeroJyIiLg0j0lc3HFV0cGDZhn+iRPN7YEDYcsWcHTusGDBAurXr8/27dsJCAhgxYoVTJ8+HV9fX8c2LCIico00x8VJYmPhiSfg7FlzOCg6+tpvfnglSUlJREVFsWjRIgBatGjBokWLtMxZRETchsf0uLiLc+dgwADo1ctMWpo1M2uzODppUW0WERHxBOpxKUIJCWZtll9+gRIlYNQoeOklKOnA74Jqs4iIiCdR4lIEDAOmTYPnnzcn49aoAYsXQ4sWjm332LFjREZGsnr1akC1WURExP0pcXGwkyfNoaHPPze3O3aEOXPMew450qpVq+jbt69qs4iIiEfRHBcH+uYbCA01kxYvL3jnHfj0U8cmLampqTz//PO0bdtWtVlERMTjeEzi4kp1XNLTzbkr99wDR4/CzTeby5z/7/+KpjbLW2+9Bag2i4iIeB6PSVxcpY7L779DeDiMHWvObRkwALZvN3teHGnhwoWEhYWpNouIiHg0zXGxo2XL4JFH4J9/oEwZmDULIiIc2+bZs2cZNGiQarOIiEix4DE9Ls504YJZ9bZbNzNpadTIXPrs6KRl27Zt1K9fX7VZRESk2FCPyzXavRt69DD/BXjxRXjtNShVynFt2mw2Jk+ezPDhw1WbRUREihUlLgWQkQEbNkBiIlSrZt5fqEQJ8w7OQ4bAxYtQpQosXAitWjk2FtVmERGR4kyJyxUsWwZPPw1//vnvvurVoVYt2LTJ3G7TBubPN5MXR1JtFhERKe6UuFzGsmXQvbu5OuhSR4+aXyVKwPjxMHSo+X9HSU1NZeTIkVnLnOvWrcuSJUu0zFlERIodj5mca+86LhkZZk9LzqTlUpUqwTPPODZpUW0WERGRf3lM4mLvOi4bNmQfHsrL8ePmcY6i2iwiIiLZaagoH4mJ9j2uMFSbRUREJG8e0+Nib9Wq2fe4glJtFhERkfwpcclH8+YQFJT/vYUsFqhZ0zzOHmw2G2+99RaNGzfmwIED1KpVi/Xr1/PSSy9htVrt04iIiIibU+KSD6sVpk41/58zecncnjLFPO5aHTt2jHbt2vH888+Tnp5Ot27dSEhIUEE5ERGRHJS4XEbXrvDxx1CjRvb9QUHm/q5dr72NVatWERoayurVq/H19WX27Nl89NFHKignIiKSB03OvYKuXaFz59yVc6+1p0W1WURERApPiUsBWK0QHm6/8+3fv5+IiAi2b98OmEu5J06cqGXOIiIiV6DEpYgtXLiQQYMGce7cOQICApgzZw6dO3d2dlgiIiJuQYlLEVFtFhERkWvnMZNz7V3y355Um0VERMQ+PCZxsXfJf3tQbRYRERH70lCRgxw7dozIyEhWr14NQLdu3Xj//fe1zFlEROQaeEyPiytRbRYRERHHUOJiR6mpqTz//PO0bduWEydOULduXbZt28Zjjz2GJb97B4iIiEiBaajITlSbRURExPGUuNiBarOIiIgUDSUu10C1WURERIqW5rhcJdVmERERKXrqcSkkm83G5MmTGT58OOnp6dSqVYuYmBiaNm3q7NBEREQ8nhKXQlBtFhEREefSUFEBqTaLiIiI86nHpYBmzpyZVZtlyZIlhISEODskERGRYsdjelwcfZPF6Ohohg0bxubNm5W0iIiIOInHJC6OvslixYoVGTdunArKiYiIOJHHJC4iIiLi+ZS4iIiIiNtQ4iIiIiJuQ4mLiIiIuA0lLiIiIuI2lLiIiIiI21DiIiIiIm5DiYuIiIi4DSUuIiIi4jaUuIiIiIjbUOIiIiIibkOJi4iIiLgNJS4iIiLiNko6OwB7MwwDgKSkJCdHImlpaZw/f56kpCRKlSrl7HDEQ+i6EkfQdeV8mX+3M/+O58fjEpezZ88CULNmTSdHIiIiIoV19uxZypUrl+/jFuNKqY2bsdlsHD16lDJlymCxWOx23oYNG7J161annquwzyvo8QU57nLH5PdYUlISNWvW5I8//qBs2bIFC9oF2PN7XZRt6bpybe54XV3LeZx1XV3t47quiq6d/M5lGAZnz56levXqlCiR/0wWj+txKVGiBEFBQXY/r9VqtdvFfLXnKuzzCnp8QY673DFXen7ZsmXd6heBPb/XRdmWrivX5o7X1bWcx1nX1bU+ruvK8e1c7lyX62nJpMm5BRQVFeX0cxX2eQU9viDHXe4Ye743rqAoX4+uK11XrtzWtZzHWdfVtT7uborq9bjC76pMHjdUJK4jKSmJcuXKcebMGbf6BCOuTdeVOIKuK/ehHhdxGG9vb1555RW8vb2dHYp4EF1X4gi6rtyHelxERETEbajHRURERNyGEhcRERFxG0pcRERExG0ocRERERG3ocRFRERE3IYSF3EJf/zxB+Hh4YSEhFCvXj0++ugjZ4ckHuKBBx6gQoUKdO/e3dmhiJtauXIlN998MzfeeCMffPCBs8Mp9rQcWlxCYmIix48f5/bbb+fEiROEhYXxyy+/4O/v7+zQxM2tW7eOc+fOMX/+fD7++GNnhyNuJj09nZCQENatW0fZsmUJCwtj8+bNBAQEODu0Yks9LuISqlWrxu233w5A5cqVCQgI4O+//3ZuUOIRWrZsSZkyZZwdhripLVu2cOutt1KjRg3KlClD+/btWbVqlbPDKtaUuEiBrF+/no4dO1K9enUsFgsrVqzIdczMmTO57rrr8PHxoUGDBmzYsOGq2tq2bRs2m42aNWteY9Ti6oryupLi6VqvsaNHj1KjRo2s7aCgII4cOVIUoUs+lLhIgSQnJxMaGsr06dPzfHzp0qUMGTKEkSNHsnPnTpo3b067du04fPhw1jENGjTgtttuy/V19OjRrGNOnTpF3759mT17tsNfkzhfUV1XUnxd6zWW12wKi8Xi0JjlCgyRQgKM5cuXZ9vXqFEj48knn8y275ZbbjGGDRtW4PNevHjRaN68ubFgwQJ7hCluxlHXlWEYxrp164xu3bpda4ji5q7mGvv++++NLl26ZD321FNPGYsXL3Z4rJI/9bjINUtNTWX79u20bt062/7WrVuzcePGAp3DMAz69evHPffcQ58+fRwRprgZe1xXIpdTkGusUaNG/Pzzzxw5coSzZ88SFxdHmzZtnBGu/E9JZwcg7u/kyZNkZGRQpUqVbPurVKnCsWPHCnSO77//nqVLl1KvXr2sMeiFCxdSt25de4crbsIe1xVAmzZt2LFjB8nJyQQFBbF8+XIaNmxo73DFDRXkGitZsiSTJk2iZcuW2Gw2XnjhBQIDA50RrvyPEhexm5zjvoZhFHgsuFmzZthsNkeEJW7uWq4rQCtA5IqudI116tSJTp06FXVYkg8NFck1q1ixIlarNden4BMnTuT6JCNSULquxNF0jbknJS5yzby8vGjQoAHx8fHZ9sfHx9OkSRMnRSXuTteVOJquMfekoSIpkHPnzvHrr79mbR86dIiEhAQCAgKoVasWQ4cOpU+fPtxxxx00btyY2bNnc/jwYZ588kknRi2uTteVOJquMQ/k3EVN4i7WrVtnALm+IiMjs46ZMWOGERwcbHh5eRlhYWHGt99+67yAxS3ouhJH0zXmeXSvIhEREXEbmuMiIiIibkOJi4iIiLgNJS4iIiLiNpS4iIiIiNtQ4iIiIiJuQ4mLiIiIuA0lLiIiIuI2lLiIiIiI21DiIiIiIm5DiYuIiIi4DSUuIuKyNm7ciMVioW3btnk+PmTIELp06VK0QYmIUylxERGXNWfOHCIiIli3bh2HDx/O9fjWrVtp1KiREyITEWfRTRZFxCUlJydTtWpV1q5dyyuvvELjxo15+eWXAUhLS8Pf35+0tLSs4xs1asTmzZudFa6IFBH1uIiIS1q6dClVq1alUaNG9O7dm7lz55L5OctqtfLdd98BkJCQQGJiIqtWrXJmuCJSRJS4iIhLio6Opnfv3gB06dKFEydOsHbtWgBKlCjB0aNHCQwMJDQ0lKpVq1K+fHknRisiRUWJi4i4nF9++YWNGzfSq1cvAEqXLk3nzp2ZM2dO1jE7d+4kNDTUWSGKiJMocRERlxMdHU3Dhg256aabsvb17t2bZcuWcfr0acAcIlLiIlL8KHEREZeSnp7OggULsnpbMrVp04YyZcqwePFiAH766Sfq1avnjBBFxIlKOjsAEZFLrVy5kuPHj3Pbbbfx888/Z3usefPmREdHM3jwYGw2Gz/++CNHjx7F39+fcuXKOSliESlKWg4tIi6lY8eOrFy58rLHbN++nT179vDiiy9y9OhRhg4dyqRJk4ooQhFxJiUuIiIi4jY0x0VERETchhIXERERcRtKXERERMRtKHERERERt6HERURERNyGEhcRERFxG0pcRERExG0ocRERERG3ocRFRERE3IYSFxEREXEbSlxERETEbfw/8O6n0g40exYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Δt = pi / 2**arange(11)\n",
    "loglog(Δt, error, 'bo-')\n",
    "loglog(Δt, Δt, 'k-')\n",
    "xlabel(\"$\\\\Delta t$\")\n",
    "legend([\"FE error $|x(\\\\pi) + 1|$\", \"$\\\\Delta t$\"])\n",
    "title(\"problem 1.3: forward-Euler convergence\")\n",
    "grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96e01a07-b5fb-430e-bbe7-8c95223b6968",
   "metadata": {},
   "source": [
    "We clearly see that the error is going to zero with $\\Delta t$: **convergence to the analytical result!**.  Furthmore, its slope matches the $\\Delta t$ line, so we have $\\boxed{O(\\Delta t)}$ convergence as expected from class.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eeb86d31-15c7-4f01-a83d-cd1b7d94eafa",
   "metadata": {},
   "source": [
    "## Problem 2\n",
    "\n",
    "Consider the following numerical integration methods:  \n",
    "\n",
    "1.  \n",
    "   $$ v^{n+1} = -4v^n + 5v^{n-1} + 4\\Delta t F(v^n) + 2\\Delta t F(v^{n-1}) $$  \n",
    "\n",
    "2.  \n",
    "   $$ v^{n+1} = v^n + \\frac{3}{2} \\Delta t F(v^{n+1}) - \\frac{1}{2} \\Delta t F(v^{n-1}) $$  \n",
    "\n",
    "- For each scheme, determine whether it is zero stable.  \n",
    "- For each scheme, determine its global order of accuracy.  \n",
    "- For each scheme, determine whether it is linearly stable in solving the equation  \n",
    "\n",
    "  $$ \\frac{du}{dt} = -\\lambda u $$  \n",
    "\n",
    "  for a real, nonnegative $\\lambda$. If your answer depends on $\\Delta t$, state the range of $\\Delta t$ for which the scheme is linearly stable.  \n"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "6a05c341-5af4-4abd-9154-8ec8a59d026c",
   "metadata": {},
   "source": [
    "## Solutions:\n",
    "\n",
    "We consider two linear multistep schemes:\n",
    "\n",
    "## Scheme 1\n",
    "$v^{n+1} = -4v^n + 5v^{n-1} + 4\\Delta t F(v^n) + 2\\Delta t F(v^{n-1})$\n",
    "\n",
    "## Scheme 2\n",
    "$v^{n+1} = v^n + \\frac{3}{2}\\Delta t F(v^n) - \\frac{1}{2}\\Delta t F(v^{n-1})$\n",
    "\n",
    "For each scheme, we will determine zero stability, global order of accuracy, and eigenvalue stability. The eigenvalue stability is checked by applying each scheme to the test equation:\n",
    "\n",
    "$\\frac{du}{dt} = -\\lambda u, \\quad \\lambda \\geq 0.$\n",
    "\n",
    "### 1. Analysis of Scheme 1\n",
    "\n",
    "#### 1.1 Zero Stability\n",
    "\n",
    "To analyze zero stability, we set $F \\equiv 0$. The method reduces to:\n",
    "\n",
    "$v^{n+1} = -4v^n + 5v^{n-1}$\n",
    "\n",
    "We can write this recurrence in terms of a 2x2 matrix and find the eigenvalues.  Equivalently, assuming a trial solution $v^n = r^n$, we get the characteristic polynomial:\n",
    "\n",
    "$r^2 + 4r - 5 = 0$\n",
    "\n",
    "Using the quadratic formula:\n",
    "\n",
    "$r = \\frac{-4 \\pm \\sqrt{16 + 20}}{2} = \\frac{-4 \\pm \\sqrt{36}}{2} = \\frac{-4 \\pm 6}{2}$\n",
    "\n",
    "This gives us roots $r_1 = 1$ and $r_2 = -5$. \n",
    "\n",
    "For zero stability, all roots must satisfy $|r| \\leq 1$, with any root satisfying $|r| = 1$ being simple. Since $|-5| = 5 > 1$, the method fails the root condition and is **not zero stable**.\n",
    "\n",
    "#### 1.2 Global Order of Accuracy\n",
    "\n",
    "To determine the order of accuracy, we perform a Taylor series analysis. Assume $v(t)$ is a sufficiently smooth solution to the differential equation $v'(t) = F(t, v(t))$. Let $v^n = v(t_n)$ where $t_n = n\\Delta t$.\n",
    "\n",
    "First, we expand $v(t_{n+1})$ around $t_n$ using Taylor series:\n",
    "\n",
    "$v(t_{n+1}) = v(t_n) + \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) + \\frac{(\\Delta t)^3}{6}v'''(t_n) + \\frac{(\\Delta t)^4}{24}v^{(4)}(t_n) + O((\\Delta t)^5)$\n",
    "\n",
    "Similarly for $v(t_{n-1})$:\n",
    "\n",
    "$v(t_{n-1}) = v(t_n) - \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) - \\frac{(\\Delta t)^3}{6}v'''(t_n) + \\frac{(\\Delta t)^4}{24}v^{(4)}(t_n) + O((\\Delta t)^5)$\n",
    "\n",
    "For $F(v^n)$, we have $F(v^n) = v'(t_n)$. For $F(v^{n-1})$, we need to expand:\n",
    "\n",
    "$F(v^{n-1}) = F(v(t_{n-1})) = v'(t_{n-1})$\n",
    "\n",
    "We can expand $v'(t_{n-1})$ using Taylor series:\n",
    "\n",
    "$v'(t_{n-1}) = v'(t_n) - \\Delta t v''(t_n) + \\frac{(\\Delta t)^2}{2}v'''(t_n) - \\frac{(\\Delta t)^3}{6}v^{(4)}(t_n) + O((\\Delta t)^4)$\n",
    "\n",
    "Now, let's substitute these expansions into the scheme:\n",
    "\n",
    "$v(t_{n+1}) = -4v(t_n) + 5v(t_{n-1}) + 4\\Delta t v'(t_n) + 2\\Delta t v'(t_{n-1})$\n",
    "\n",
    "Substituting the Taylor series:\n",
    "\n",
    "$v(t_n) + \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) + \\frac{(\\Delta t)^3}{6}v'''(t_n) + \\frac{(\\Delta t)^4}{24}v^{(4)}(t_n) + O((\\Delta t)^5)$\n",
    "\n",
    "$= -4v(t_n) + 5\\left[v(t_n) - \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) - \\frac{(\\Delta t)^3}{6}v'''(t_n) + \\frac{(\\Delta t)^4}{24}v^{(4)}(t_n) + O((\\Delta t)^5)\\right]$\n",
    "\n",
    "$+ 4\\Delta t v'(t_n) + 2\\Delta t \\left[v'(t_n) - \\Delta t v''(t_n) + \\frac{(\\Delta t)^2}{2}v'''(t_n) - \\frac{(\\Delta t)^3}{6}v^{(4)}(t_n) + O((\\Delta t)^4)\\right]$\n",
    "\n",
    "Expanding and collecting like terms, we see that terms match up to and including $O((\\Delta t)^3)$, but differ at $O((\\Delta t)^4)$. Therefore, the truncation error is $O((\\Delta t)^4)$, making the scheme **third-order accurate**.\n",
    "\n",
    "#### 1.3 Linear Stability\n",
    "\n",
    "For the test equation $F(v) = -\\lambda v$, the scheme becomes:\n",
    "\n",
    "$v^{n+1} = (-4 - 4\\lambda\\Delta t)v^n + (5 - 2\\lambda\\Delta t)v^{n-1}$\n",
    "\n",
    "The characteristic polynomial is:\n",
    "\n",
    "$r^2 + (4 + 4\\lambda\\Delta t)r - (5 - 2\\lambda\\Delta t) = 0$\n",
    "\n",
    "For eigenvalue stability, we need all roots to satisfy $|r| \\leq 1$. Let's analyze the roots as $\\lambda\\Delta t$ varies:\n",
    "\n",
    "When $\\lambda\\Delta t = 0$, we already know that one root has magnitude 5, which exceeds 1.\n",
    "\n",
    "To see how the roots behave as $\\lambda\\Delta t$ increases, let's compute the roots for specific values:\n",
    "\n",
    "1. For $\\lambda\\Delta t = 0$: Roots are $r = 1$ and $r = -5$ with max magnitude = 5\n",
    "2. For $\\lambda\\Delta t = 1$:\n",
    "   Characteristic equation: $r^2 + 8r - 3 = 0$\n",
    "   Using the quadratic formula: $r = \\frac{-8 \\pm \\sqrt{64+12}}{2} = \\frac{-8 \\pm \\sqrt{76}}{2} \\approx \\frac{-8 \\pm 8.718}{2}$\n",
    "   Giving roots $r \\approx 0.359$ and $r \\approx -8.359$ with max magnitude ≈ 8.359\n",
    "3. For $\\lambda\\Delta t = 2$:\n",
    "   Characteristic equation: $r^2 + 12r - 1 = 0$\n",
    "   Roots: $r = \\frac{-12 \\pm \\sqrt{144+4}}{2} = \\frac{-12 \\pm \\sqrt{148}}{2} \\approx \\frac{-12 \\pm 12.166}{2}$\n",
    "   Giving roots $r \\approx 0.083$ and $r \\approx -12.083$ with max magnitude ≈ 12.083\n",
    "\n",
    "On plotting the root magnitude against various values of $\\lambda\\Delta t$ below, we see that as $\\lambda\\Delta t$ increases, the maximum root magnitude grows. Since the scheme already has an unstable root at $\\lambda\\Delta t = 0$, increasing $\\lambda\\Delta t$ only makes the instability worse.\n",
    "\n",
    "Therefore, Scheme 1 is **eigenvalue unstable for all $\\lambda\\Delta t > 0$**.\n",
    "\n",
    "## 2. Analysis of Scheme 2\n",
    "\n",
    "### 2.1 Zero Stability\n",
    "\n",
    "Setting $F \\equiv 0$, the method reduces to:\n",
    "\n",
    "$v^{n+1} = v^n$\n",
    "\n",
    "The characteristic equation is $r - 1 = 0$, with a simple root $r = 1$. Thus, **zero stability holds**.\n",
    "\n",
    "### 2.2 Global Order of Accuracy\n",
    "\n",
    "Using Taylor series analysis as before:\n",
    "\n",
    "$v(t_{n+1}) = v(t_n) + \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) + \\frac{(\\Delta t)^3}{6}v'''(t_n) + O((\\Delta t)^4)$\n",
    "\n",
    "$v(t_{n-1}) = v(t_n) - \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) - \\frac{(\\Delta t)^3}{6}v'''(t_n) + O((\\Delta t)^4)$\n",
    "\n",
    "$F(v^n) = v'(t_n)$\n",
    "\n",
    "$F(v^{n-1}) = v'(t_{n-1}) = v'(t_n) - \\Delta t v''(t_n) + \\frac{(\\Delta t)^2}{2}v'''(t_n) + O((\\Delta t)^3)$\n",
    "\n",
    "Substituting into the scheme:\n",
    "\n",
    "$v(t_{n+1}) = v(t_n) + \\frac{3}{2}\\Delta t v'(t_n) - \\frac{1}{2}\\Delta t v'(t_{n-1})$\n",
    "\n",
    "$v(t_n) + \\Delta t v'(t_n) + \\frac{(\\Delta t)^2}{2}v''(t_n) + \\frac{(\\Delta t)^3}{6}v'''(t_n) + O((\\Delta t)^4)$\n",
    "\n",
    "$= v(t_n) + \\frac{3}{2}\\Delta t v'(t_n) - \\frac{1}{2}\\Delta t \\left[v'(t_n) - \\Delta t v''(t_n) + \\frac{(\\Delta t)^2}{2}v'''(t_n) + O((\\Delta t)^3)\\right]$\n",
    "\n",
    "On expanding and collecting terms, we see that terms match up to and including $O((\\Delta t)^2)$, but differ at $O((\\Delta t)^3)$. Therefore, the truncation error is $O((\\Delta t)^3)$, making the scheme **second-order accurate**.\n",
    "\n",
    "### 2.3 Eigenvalue Stability\n",
    "\n",
    "For the test equation $F(v) = -\\lambda v$, the scheme becomes:\n",
    "\n",
    "$v^{n+1} = v^n - \\frac{3}{2}\\lambda\\Delta t v^n + \\frac{1}{2}\\lambda\\Delta t v^{n-1}$\n",
    "\n",
    "Rearranging:\n",
    "\n",
    "$v^{n+1} = (1 - \\frac{3}{2}\\lambda\\Delta t) v^n + \\frac{1}{2}\\lambda\\Delta t v^{n-1}$\n",
    "\n",
    "The characteristic equation is:\n",
    "\n",
    "$r^2 - (1 - \\frac{3}{2}\\lambda\\Delta t)r - \\frac{1}{2}\\lambda\\Delta t = 0$\n",
    "\n",
    "On analyzing the roots for different values of $\\lambda\\Delta t$ based on the plot below, we see that as $\\lambda\\Delta t$ increases, the maximum root magnitude grows beyond 1, indicating instability. At $\\lambda\\Delta t = 2$, the maximum root magnitude is exactly 1 (when calculated precisely), representing the stability boundary.\n",
    "\n",
    "To determine the exact stability range, we need to find when the magnitude of at least one root exceeds 1. The transition happens at $\\lambda\\Delta t = 2$, after which the scheme becomes unstable.\n",
    "\n",
    "Therefore, Scheme 2 is **linearly stable for $0 \\leq \\lambda\\Delta t \\leq 2$**.\n",
    "\n",
    "\n",
    "\n",
    "![image.png](attachment:d1c1eba3-8df1-48da-aba9-be929003aad6.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59b1eae4-1c7e-408c-8c28-f306ae36e912",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "fc6539cf-aad6-4760-80fc-e4ecbf7188be",
   "metadata": {},
   "source": [
    "## Problem 3\n",
    "\n",
    "A reasonable model of the velocity $v(t)$ of a skydiver is\n",
    "\n",
    "$ \\frac{dv}{dt} = -g + \\frac{k}{m} v^2, \\quad v(0) = 0, $\n",
    "\n",
    "where $g = 9.8 \\, \\text{m/sec}^2$ is gravitational acceleration, $m$ is the mass of the skydiver with parachute, and $k$ quantifies the effect of air resistance. At the US Air Force Academy, a training jump starts at about 1200 m and has $k = 0.4875$ for $t < 13$ and $k = 29.16$ for $t \\geq 13$. (This is an oversimplification; see Meade & Struthers (1999).)\n",
    "\n",
    "(a) Solve the IVP for $v$ for an 80-kg cadet for $t \\in [0,200]$, and plot the solution.\n",
    "\n",
    "(b) Suppose we also want the altitude h, satisfying $dh/dt = -v$.   Write a combined system of ODEs du/dt = f(u,t) for the vector u = [v, h].  (What is the right-hand-side f(u,t) and the initial condition u(0)?)   Plug this system into your numerical solver algorithm from part (a) and plot the resulting h(t) (from the second component of the solution).\n",
    "\n",
    "(c) You should have found that the altitude h becomes negative at some point.  How would you determine, consistent with your approximate solver in part (b), the time t at which h(t)=0? (i.e. when does the skydiver hit the ground?).   (Hint: what interpolation between data points $t_n, u_n$ is implied by your numerical method?)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c067df5",
   "metadata": {},
   "source": [
    "### Solutions\n",
    "**(a)** The forward Euler method was implemented and used to solve the IVP. The solution is plotted below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c45fa902-5875-4813-ae74-086871396a6b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "g, m = 9.8, 80\n",
    "k = lambda t: 0.4875 if t<13 else 29.16\n",
    "dv_dt = lambda u, t: np.array([-g + k(t) * u[0]**2 / m]) #u = [v]\n",
    "dt = 2e-4\n",
    "def forward_euler(F, u0, t_end = 200, dt=dt):\n",
    "    u, t, dim = u0, 0, len(u0)\n",
    "    N = math.ceil(t_end/dt)\n",
    "    u_history = np.zeros((N+1, dim))\n",
    "    u_history[0,:] = u\n",
    "    for i in range(1,N+1):\n",
    "        u += F(u, t) * dt\n",
    "        t = i*dt\n",
    "        u_history[i,:] = u\n",
    "    return u_history\n",
    "    \n",
    "v_history = forward_euler(dv_dt, [0])\n",
    "\n",
    "plt.plot(np.arange(0,200+dt,dt), v_history[:,0])\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Velocity [m/s]')\n",
    "plt.title('Problem 3a: skydiver velocity')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea8a442d",
   "metadata": {},
   "source": [
    "**(b)** With $u = [v, h]$, we have $du/dt = [dv/dt, dh/dt] = [-g + \\frac{k}{m} v^2, v]$. Using the solver implemented above, we obtain the following plot for height."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4c063981",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "du_dt = lambda u,t: np.array([-g + k(t) * u[0]**2 / m, u[0]]) #u = [v, h]\n",
    "    \n",
    "vh_history = forward_euler(du_dt, [0, 1200])\n",
    "h_history = vh_history[:,1]\n",
    "plt.plot(np.arange(0,200+dt,dt), h_history)\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Height [m]')\n",
    "plt.title('Problem 3(b): skydiver height vs. time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6deb3d1f",
   "metadata": {},
   "source": [
    "**(c)** Forward Euler corresponds to linear interpolation of consecutive data points: $u_{i+1} = u_i + F(u_i, t_i)\\Delta t + O(\\Delta t^2)$. We can first determine the index $j$ such that $u_j >0$ and $u_{j+1} < 0$. Then, due to linear interpolation, we can find the x-intercept of the line joining $(t_j, h_j)$ and $(t_{j+1}, h_{j+1})$: $t_z = t_j + \\frac{\\Delta t h_j}{h_j-h_{j+1}} \\approx 164.99$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "521fdde1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "164.99036292911737"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = len(h_history)\n",
    "for j in range(N):\n",
    "    if h_history[j]*h_history[j+1] < 0:\n",
    "        break\n",
    "h_l, h_r = h_history[j], h_history[j+1]\n",
    "t_l, t_r = j*dt, (j+1)*dt\n",
    "t_z = t_l + dt*h_l/(h_l-h_r)\n",
    "t_z"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}